Scalable Representation - Scientific Visualization: Uncertainty, Multifield, Biomedical, and Scalable Visualization - page 357

30.1.2 Wavelets
As a hierarchical data representation for comparison, there is an approach, wavelet
[ 3 , 6 , 15 , 26 , 27 , 35 - 37 ]. In the area of volume encoding, most work [ 15 , 26 , 27 ]
has been performed for regular grids and shows effective 3D compressed volumes
and rendering. Recently, this research has been extended to irregular grids organized
using polygonal meshes [ 6 , 36 , 37 ]. Thewavelet encoding of irregular grids is usually
performed using irregular sampling and adaptive subdivision. However, the wavelet
for the irregular data set is based on polygonal meshes. Therefore, it is not easily
extended to arbitrary scattered volume data. Sohn et al. [ 35 ] presented a compression
scheme for encoding time-varying isosurface and volume features. They encoded
only the significant blocks using a block-based wavelet transform.
30.1.3 Spherical Harmonics
Most of the work in spherical harmonics has been done for surface fitting, especially,
3D object modeling and molecular surface modeling. For 3D object modeling [ 7 ,
18 , 38 ], the datasets were decomposed into high and low frequency components
and represented by the properties of the spherical harmonic basis functions. Also
this modeling was used for shape deformation [ 8 , 9 ]. In molecular surface mod-
eling [ 22 ], spherical harmonics give a sequence of smooth approximations to the
molecular surface since the shapes of the spherical harmonics are very similar to the
shapes of the molecules. For volume fitting, Misner [ 24 ] showed spherical harmonic
decomposition, however, the volume fitting is based on a rectangular grid.
30.1.4 Time Series Data Representations
The large volume of time-varying data makes visualization a challenging problem.
Many techniques for volume rendering of time-varying data have been proposed and
these techniques enable the visualization of large amount of time-varying datasets.
One approach is to use data coherency between consecutive time steps to speed up
volume rendering [ 1 , 2 , 33 , 34 ]. Another approach is to encode and compress the
time-varying data appropriately for the volume rendering [ 20 , 21 , 35 , 42 ]. Shen
and Johnson [ 34 ] proposed an algorithm that exploits data coherency between time
steps and extracts the differential information for biomedical and computational fluid
dynamics datasets. Shen et al. [ 33 ] showed the time-space partitioning (TSP) tree and
this structure improves the rendering speed and reduces the amount of volumetric
data I/O. For temporal compression approach, Westermann [ 42 ] proposed a memory
minimizing algorithm based on multi-resolution representations of both the spatial
distribution and the time evolutions. Ma and Shen [ 21 ] presented quantization and